Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
- Related Primary Literature
- Additional Reading
A member of the class of curves that are intersections of a plane with a cone of revolution. The ellipse is obtained when the plane cuts all the elements of one nappe, and does not go through the apex. In the illustration, denote the distance between two points, F, F′ of a plane by 2c, c > 0, and let 2a be a constant, with a > c. The ellipse with foci F and F′ and major axis 2a is the locus of points P of the plane such that PF + PF′ = 2a, where PF denotes the distance of P and F. This suggests the following construction of an ellipse. Put pins at F and F′, and slip over them a loop of thread of length 2a + 2c, pulling the thread taut with a pencil. If the pencil is moved, keeping the thread taut, its point traces an ellipse. Another way to construct an ellipse is to drill a hole in a stick (at any point other than the midpoint) and move the stick so that its ends slide along two mutually perpendicular lines. The point of a pencil inserted in the hole will trace an ellipse. Limiting forms of the ellipse are (1) a circle, as the two foci approach coincidence, and (2) the segment FF′, as c approaches a. If a circle is projected orthogonally on a plane not parallel to the plane of the circle, an ellipse is obtained, and every ellipse may be so obtained. Lines joining the foci to a point P of an ellipse make equal angles with the tangent to the ellipse at P, and consequently light or sound that emanates from one focus is reflected to the other focus. This property is used in construction of “whispering galleries.” See also: Conic section
The content above is only an excerpt.
for your institution. Subscribe
To learn more about subscribing to AccessScience, or to request a no-risk trial of this award-winning scientific reference for your institution, fill in your information and a member of our Sales Team will contact you as soon as possible.
to your librarian. Recommend
Let your librarian know about the award-winning gateway to the most trustworthy and accurate scientific information.
AccessScience provides the most accurate and trustworthy scientific information available.
Recognized as an award-winning gateway to scientific knowledge, AccessScience is an amazing online resource that contains high-quality reference material written specifically for students. Contributors include more than 9000 highly qualified scientists and 43 Nobel Prize winners.
MORE THAN 8700 articles covering all major scientific disciplines and encompassing the McGraw-Hill Encyclopedia of Science & Technology and McGraw-Hill Yearbook of Science & Technology
115,000-PLUS definitions from the McGraw-Hill Dictionary of Scientific and Technical Terms
3000 biographies of notable scientific figures
MORE THAN 19,000 downloadable images and animations illustrating key topics
ENGAGING VIDEOS highlighting the life and work of award-winning scientists
SUGGESTIONS FOR FURTHER STUDY and additional readings to guide students to deeper understanding and research
LINKS TO CITABLE LITERATURE help students expand their knowledge using primary sources of information